On angle-of-arrival and time-of-arrival statistics of geometric scattering channels

This paper proposes a hyperbolic distribution to model the distribution of random scatterers between a base station (BS) and the user equipment (UE) in multipath mobile environments. New hyperbolic angle-of-arrival (AoA) probability density function (pdf), power azimuth spectrum (PAS), time-of-arrival (ToA) pdf, and power delay spectrum (PDS) are derived. The effectiveness of Gaussian, Janaswamy, and hyperbolic scatterer distributions is assessed by estimating their fitting errors to a given empirical data set. New 3-D simulation results on the Gaussian and hyperbolic PAS and PDS are given and discussed. The line-of-sight (LoS) distance D (in kilometers) between the BS and the UE and the propagation path distance mu (in kilometers) can be related mathematically.